1171 



6. For the defermiiiation of the coeflicien(s //,,o , • • , F^.o , //;>,-i , 

 V^-i the following formulae result from (13): 



+ 00 



2 /^_o sin (tir -|- px) 



= —'-— 3— 2: [Cj,ocos{'UT -{- pt) ^ C ocosOw -üt)|, 



+" , . , e dCoo d6, 



£ //y s''« (^ + pr) = — — ^ sin tü* -— ■ -f- 



4_ _!_ ^^ïf p^/'.O 5in {^ \ pr) dC_^,,o .«« (tiT— pr)" 

 a'A,r, dr ;,=i |_ 



(27) 



d^ 



Ö9 



P 



(28) 



+ 



^ Illpfi sin {IJT -f pr) =z -— Co 



-00 «^iX, 





C03 tcr, (29) 



+« 



2 IVpfisin {^\-pT) z= 



e' dv, d<9. /'=« 



1 ^ 



a'A,r,» 0^ dr ^,^1 



5m (tcr 4- pr) sin (Ttr — pr) 



/'»o :: ^-/^.ü — — 



p 



^ F^^O 'in {iJr -\- px) z= j-^ —L- —J. sin TOT 



+«, 

 •2" JIp-i sin ('ÏU" f px) 



— 00 



2 F//, - 1 sin (TtT --)- jot) = 



a' A, X,' d^ dr 



e' ÖC00 06». 



-— — — sin 17——, 



aAjX, dq Ox 



^0,0 ^ — Sin tlT 



a'A.^"'"x,'Ö7 



(31) 

 (32) 

 (33) 



In taking the derivatives in the right members of these formulae 

 the corresponding qnantitities are to be considered as functions of 

 Q„o„ q and t. 



The values of I,,fi , . . , F 0, (9^')f resulting from (27)— (31) and 

 (20) have been collected in the tirst table of the next page. 



The coefificients 6»; , '''^' result from the equation 



1 idCo.o CoodX 



^ _ sin ('C7 -(- ^t) =^- ^ s 



be, 



-^ J sin tC — -^; (34) 



here, in taking the derivatives, p, is to be considered constant. 

 Hence : 



<9j-^''" = 0, 9 = 0, ±1, ±2..... (35) 



The values of the coefficients with odd index have been collected 

 in the second table of the next page. 



